31) Verify that Stokes' Theorem is true for the vector field F(x,y,z) = x² i + y² j + z² k, where S is the part of the paraboloid z 1 - x² - y ² that lies above the xy-plane and S has an upward orientation. 2

Q: Let S be the part of paraboloid z = 9 – x2 - y? with z 2 0. Verify Stokes' theorem for vector field…

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Q: Compute feF. dr where C is the curve of intersection of the paraboloid z=9-x² - y² and the plane z =…

A: To compute the line integral ∫CF⋅dr. We have F=2x2+3zi+4ey+8xj+6z2+7yk and  C is the curve of…

Q: Use (a) parametrization; field (b) Stokes' Theorem to compute fF. dr for the vector F = (x²+z)i +…

A: Given:F=(x2+z)i+(y2+2x)j+(z2-y)kC: intersection of x2+y2+z2=1 and z= x2+y2

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: F(x, y, z) = (x²)Î + (2y³2)ĵ + (32)Â is a vector field. (a) div(F) (b) curl(F) (c) C is the…

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Q: Verify Stokes theorem for the vector field F = 2(-+x)i- z? yj-zyk over the upper half x² +y? +z?…

A: To verify Stokes' Theorem for the vector field               F→=2-y2+xi→-z2yj→-zy2k→ over the upper…

Q: A) Consider the vector field F(x, y, z) = (-3yz, 6xz, xy). Find the divergence and curl of F. 0…

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Q: A vector field is given by A(x,y,z)=xyi+2yzj+3zxk. In this multi-part question we will check that…

A: Here, the vector field, A(x,y,z)=xy i + 2yz j + 3zx k. So, the curl A=ijk∂∂x∂∂y∂∂zxy2yz3zx ⇒curl…

Q: Vector Field: F(x,y) = (xv, 3x, – 2y) and Surface: z = 4 - x - 3 y? Use the normal vector formula to…

A: Given surface z=4-x-3y2

Q: Let F = xyi + yzj + zæk be a vector field. Use Stokes' Theorem to evaluate f. F . dr where C is the…

A: Given that,F=xyi+yzj+zxkand the given plane is,x+y+z=1

Q: Compute the unit normal vector field that will give the surface parametrized by r(u, v) = (e"…

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Q: a) Is the vector field F = (sin z, y², x cos z) conservative? Explain your reasoning. b) Compute the…

A: According to the given information, (a)

Q: 2) Check Stoke's theorem using the vector field A = origin in the xy plane. ayx + bxy, where a and b…

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Q: 26. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y+z)k and surface z = 4x² - y², z ≥…

A: The given problem is to verify the stokes theorem for the given vector field over the given surface…

Q: 1: Let Let F = (yz², tan-1(xy), 1 + xy³). %3D a) Show that F is not conservative. b) Show that F…

A: conservative vector field is a vector field that is the gradient of function

Q: Show that the regular surface S = {(x, y, z): x² + y² = 2² + 1, x > 0 or y > U} is orient: by…

A: A regular surface is a mathematical object that locally looks like a piece of a plane, meaning that…

Q: please answer fully on paper and make sure its correct please i keep getting different answers

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Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

A: The vector field is, F⇀x,y,z=x,y,z. The region is bounded by the paraboloid z=3-x2-y2 and the plane…